Q.A sonometer wire of length $1.5\ \text{m}$ has a mass of $15\ \text{g}$ and is kept under a tension of $300\ \text{N}$. Calculate the speed of a transverse wave along the wire.

Given: $L=1.5\ \text{m}$, $m=15\ \text{g}=0.015\ \text{kg}$, $T=300\ \text{N}$.

Mass per unit length: $\mu=\frac{0.015}{1.5}=0.01\ \text{kg m}^{-1}$

Wave speed: $v=\sqrt{\frac{T}{\mu}}=\sqrt{\frac{300}{0.01}}=\sqrt{30000}\approx173.2\ \text{m s}^{-1}$

Compute $\mu=m/L$ in $\text{kg m}^{-1}$, then substitute into $v=\sqrt{T/\mu}$.

• Not converting grams to kilograms before dividing by length.
• Mis-simplifying $300/0.01$ (a common slip is losing a factor of $10$ or $100$).